This program generates a network of LIF neurons which are connected through chemical synapses. It solves LIF equation as follows:
where τ is the time constant of neuron, v is the membrane potential of the postsynaptic neuron, vrest is the resting state membrane potential, I_ext is the external input, which is equivalent to a sensory stimulus or any input sourced from the activity of population of neurons nearby, and Isyn is accumulative synaptic inputs arrived from all the pre-synaptic neurons to the given post-synaptic one, which is calculated through
here, i is associated index of pre synaptic neurons, v is the postsynaptic potential, and Esyn is the synaptic reversal potential. Whether a synapse is excitatory or inhibitory is determined by Esyn. For inhibitory synapses, Esyn equals to E_syn_inh (here it is -80), and for excitatory ones the value is set to zero. g is maximal conductance of the synapse, and S represents the fraction of bound receptors. Its kinetics are described by the following equation,
where N is equivalent to the concentration of transmitters released into the synaptic cleft following the arrival of an action potential at the pre-synaptic terminal. Since the concentration of neurotransmitters in the cleft rises and falls very rapidly, it is assumed that N occurs as a rectangular pulse. α and β are the rate constants for transmitter binding to and unbinding from post-synaptic receptor, respectively. α and β and duration of N characterize the dynamics of post-synaptic potential (EPSP & IPSP). They directly specify the shape of S. (Destexhe, 1993)
This program returns 4 graphs. Figure(1) depicts the sub-threshold dynamics of neurons' membrane potential. Figure(2) represents the dynamics of N. It also shows the dynamics of S12 and S21, which is meant to demonstrate the typical profile of S signal, which in turn determine the input Isyn. You can produce EPSP and IPSP corresponding to NMDA, GABAA, GABAB, etc. by setting relevant values for α and β and therefore for the shape the S profile. Figure(3) demonstrates the accumulative synaptic inputs from pre-synaptic neurons arrived to the post-synaptic ones. Note that negative Isyn corresponds to EPSP and positive Isyn corresponds to IPSP (Consider the negative sign before Isyn in the LIF equation). Figure(4) is raster plot of the neuronal activity in the network.